2/6 Additive Inverse :

The additive inverse of 2/6 is -2/6.

This means that when we add 2/6 and -2/6, the result is zero:

2/6 + (-2/6) = 0

Additive Inverse of a Fraction

For fractions, the additive inverse is found by negating the numerator or denominator, but not both. In this case:

  • Original fraction: 2/6
  • Additive inverse: -2/6

To verify: 2/6 + (-2/6) = 0

Extended Mathematical Exploration of 2/6

Let's explore various mathematical operations and concepts related to 2/6 and its additive inverse -2/6.

Basic Operations and Properties

  • Square of 2/6: 0.11111111111111
  • Cube of 2/6: 0.037037037037037
  • Square root of |2/6|: 0.57735026918963
  • Reciprocal of 2/6: 3
  • Double of 2/6: 0.66666666666667
  • Half of 2/6: 0.16666666666667
  • Absolute value of 2/6: 0.33333333333333

Trigonometric Functions

  • Sine of 2/6: 0.32719469679615
  • Cosine of 2/6: 0.94495694631474
  • Tangent of 2/6: 0.34625354951058

Exponential and Logarithmic Functions

  • e^2/6: 1.3956124250861
  • Natural log of 2/6: -1.0986122886681

Floor and Ceiling Functions

  • Floor of 2/6: 0
  • Ceiling of 2/6: 1

Interesting Properties and Relationships

  • The sum of 2/6 and its additive inverse (-2/6) is always 0.
  • The product of 2/6 and its additive inverse is: -4
  • The average of 2/6 and its additive inverse is always 0.
  • The distance between 2/6 and its additive inverse on a number line is: 4

Applications in Algebra

Consider the equation: x + 2/6 = 0

The solution to this equation is x = -2/6, which is the additive inverse of 2/6.

Graphical Representation

On a coordinate plane:

  • The point (2/6, 0) is reflected across the y-axis to (-2/6, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 2/6 and Its Additive Inverse

Consider the alternating series: 2/6 + (-2/6) + 2/6 + (-2/6) + ...

The sum of this series oscillates between 0 and 2/6, never converging unless 2/6 is 0.

In Number Theory

For integer values:

  • If 2/6 is even, its additive inverse is also even.
  • If 2/6 is odd, its additive inverse is also odd.
  • The sum of the digits of 2/6 and its additive inverse may or may not be the same.

Interactive Additive Inverse Calculator

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